Finding the Lowest Common Denominator

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Step 1: See if the smaller denominator divides into the larger denominator with no remainder.

Say we want to add:

eq001

Because 9/3 = 3, the lowest common denominator is 9. After that we do:

eq002

because 3/3 = 1. Then we replace 1/3 by 3/9 in the problem.

Eq003

Step 2: If step 1 doesn't work, we use the Euclidean Algorithm to first find the largest divisor of both numbers. Say we add:

Eq004

using the Euclidean Algorithm, we find that 3 is the largest divisor of 12 and 9. We then follow these steps:

1. Divide the first denominator by 3.

Eq005

2. Multiple the second fraction by 4/4 because 4 was the answer from the division.

Eq006

3. Divide the second denominator by 3.

Eq007

4. Multiple the first fraction by 3/3 because 3 was the answer from the second division.

Eq008

5. Add the two fractions with the common denominator.

Eq009